Answer
a. $141.6$
b. Overestimates the average yearly increase by $5.1$
Work Step by Step
a) Using the formula $$f(x)=1.1x^3-35x^2+264x+557$$ we can determine the values
$f(4)=1120.4$ and
$f(0)=557$.
Therefore, by inserting it into the slope formula $$m=\frac{f(x_{2})-f(x_{1})}{x_{2}-x_{1}}=\frac{1120.4-557}{4-0}=141.6$$
b) Because the average yearly increase determined in Exercise $27$ was $136.5$ and the result obtained using the slope was $141.6$, it follows that the slope from part $(a)$ overestimates the average yearly increase determined in exercise 27 by $141.6-136.5=5.1$.